The Flow a Fin Experiences

There's something that never seems to make into discussions about fin design and maybe for good reasons. I know I've struggled with it for a long time.

Something changes

Consider, in waist to chest high water, let a wave pass over you. Is the flow the same on the leading face as it is on the back of the wave-form? No? How about half way through? No? So, somewhere between the leading face and the back of the wave-form something changed.

Penetration matters

It's not unreasonable to assume that flow of water in a wave-form will vary with penetration into the wave-form. (When you really think about it, how could it not.) In particular, that the water particles moving on the face of the wave are moving differently that those immediately adjacent to them as you penetrate into the wave. That is, if you stuck a series of devices that measured both the magnitude and direction of flow along the penetration length of the fin, these quantities are likely to change as you move along the length of the fin. It's also not unreasonable that the magnitude of the upward component of the flow along the fin would decrease as you penetrate deeper into the wave. If so, then surely this would have implications with respect to fin design. (You'll also have to factor into the consideration the flow that is being diverted by the bottom of the surfboard. And the depth of influence of this flow is likely to be a function of the wetted surface area of the board, as well as the wave-side rail geometry.)

Forces develop on the fin from the various flows it experiences. But if the flow is different with penetration into the wave face, than the fin itself will experience different flows along its penetration length, and hence different forces will be generated. That is, different forces would be generated from those if you assumed the fin was experiencing the same flow over the whole length of penetration.

So regardless how you've decided or believe how a fin is operating, how it functions is surely flow dependent, and therefore one might expect there would be some need to account for the differences in flows with respect to penetration (assuming the changes in the flow field are sufficiently significant). For example, holding base length and rake constant, then maybe whatever the impact that one might count on for a given surface area has to be adjusted simply because the flow is changing with penetration depth.

But its not just the magnitude of the flow that would be changing.

There's also the consideration that once you start moving transversely across the face of the wave, the flow takes on that transverse component -i.e. it will be a function of both the upward flow and transverse flow (at least). So the direction of the flow, when moving transversely also stands to change with depth.

… fun, and exciting, but maybe it's delusion..

Modeling fins after dolphins, aircraft wings, etc. is very romantic and, I guess kind of exciting. It allows the designer to attribute all sorts of properties to the fin. But maybe it's delusion. Maybe the flow dynamics on a wave are sufficiently different to warrant their own approach. (Dolphins can be seen playing in waves, but its very unlikely their brief time spent in heavily shoaling or braking waves would have had much of an impact on their evolution. And I'm fairly confident that the same is true for just about any other aquatic or semi-aquatic creature.)

Surfboard fins themselves have had a kind of Darwinian evolution however, and it quite likely that many of the more popular fin styles, in many ways already take this differential flow profile into account. Or perhaps it's been discovered by the somewhat random trial and error that, the difference in flow as you penetrate into the wave may not be enough to have much of an impact.

If you survey the more popular surfboard fin designs, it's apparent that they have a lot in common. So, for example, at least over the ranges of penetration depth that you encounter today on say on the more popular shortboard fins, perhaps whatever influence this differential flow might have has been accounted for in their design (as best they could be.)

Rails Plane

Surfboard design elements or components interact differently with the different flows.

That a rail, in particular a wave-side rail, when a surfer is traveling transversely across the wave-face will plane along the wave-face, would seem to be an important consideration in the design of surfboard rails.  And, as outlined in prior posts ("The Deceleration Wave" and "What Makes Surfboards Go") different sections of the wave-side rail will be subject to different flows, and therefore experience different levels of planing.

When traveling transversely, the wave-side rail will plane.

As discussed in a prior post ("What Makes Surfboards Go"), planing will occur whenever you move a partially submerged somewhat solid object through a liquid, or move a liquid by a partially submerged object. So if you are traveling transversely and on one side you're moving partially submerged through a vertical face of water (or at some other less than vertical angle) that portion which is partially submerged will experience a planing force directed out of the face of that wall of water.  It well appreciated by surfers that “boxy” rails (excessively thick rails which present a large surface to the wave-face) will make transverse motion across a wave-face more difficult to maintain. The dropped-rails seen on SUPs or even the rolled decks seen on some surfboards are often used to get around this problem – an attempt to reduce the planing surface of the rail.

The rail profile and surface area requirements presented to the fluid (upon and in which planing occurs) tends to vary as you move from nose to tail on a surfboard. For example, the mid-section rail, when moving transversely will experience a greater forward flow than the tail region (see, post "Drag Keeps Surfers Connected to A Decelerating wave") and will often appear to be buried far deeper in the face of the wave than that of the tail section. Each section having its own combination of flows to deal with.

What Makes Surfboards Go

Surfers or surfboards redirect the forces of  planing.

Planing is often associated with high-speed boating, but in fact, any partially submerged relatively rigid object in a flow will experience planing.

The phenomena has been explored extensively in water-craft hull design. Savistsky was one of the first to fully explore and approach the subject empirically and, to a lesser extent, analytically - his work remains the basis for much of what followed in the field.  Below is his simplified illustration illustrating the forces at play during planing.

Here, Savistsky, in cross-sectional view, illustrates a simple plank moving horizontally over some water (or other liquid surface). (But because such considerations are relative, you could equivalently view the above illustration as water flowing past a stationary plank.) If we consider the case in which the plank is moving, the means by which it is moving is assumed to be via some external power source, say an inboard or outboard engine, or perhaps the plank is being pulled along, or maybe its means of propulsion is from sail.

The key point in the diagram however is that the forces of planing generated by motion through the fluid, or by the fluid flowing past the the object, are up and back (back as in the direction of the flow relative to the plank, generally in the direction which you would associate with the term 'drag'.  An engineer would say that the resulting force of planing will have both 'lift' and 'drag' components.)

But this diagram needs to be altered for surfing. Surfers generally don't have a outboard engine (though admittedly now kites and sails are often used.) The fix however is simple, just rotate the diagram.

Surfboards derive their means of propulsion by getting in the way of flow.

The inclined surface is now the face of the wave, the water moving both upward, as well as forward. And now it can be seen that the planing forces have a component in the direction of that forward motion. (The diagram here doesn't include the forces that arise from the interaction with the forward movement of water, which actually decelerating, see "The Decelerating Wave-Form".) But more importantly, there is no need to assume the existence of an external power source, like an outboard engine.  The flow is the result of the upward acceleration of water of the shoaling wave - and the propulsion comes from the surfboard's surfaces redirecting the forces of planing. And it is this redirection of the forces of planing that makes a surfboard go, at least under most conditions. In fact, it is what separates the sport from other more 'gravity reliant' sports, like snowboarding. Snowboarders don't move by getting in the way of the snow, however surfboards move by getting in the way of the flow. 

How these forces are redirected is up to the surfer, and will depend on how he chooses to present the bottom surfaces of his surfboard to the flow. In particular, its quite possible to redirect them so that there is a component of force in the transverse direction. (To visualize this, think of your flatten hand subject to a jet of water. What direction would you hand tend to move if you angled it relative to the on-coming jet?)

Gravity plays a crucial role in the dynamics.

A surfer's connection to his board is tenuous, unless he's strapped in, or has grabbed a rail. Under most circumstances, if orientated correctly, gravity will keep him on his surfboard. This isn't to say, that at other times, other forces aren't contributing.

However, gravity also plays additional roles.  It is used as a counter force against the forces of planing, keeping the surfer in the upward flow on the wave face. In addition, it is also used as a means of acquiring additional kinetic energy, by sliding down the wave-face, much like a sleigh sliding down a hill. And though gravity plays a crucial ever-present role in the dynamics, for the most part, gravity itself isn't what allows a surfer to move transversely across the face. Those forces come from the redirecting the forces of planing (as described above.)

Modern surfing styles tend to utilize gravity as an additional source of kinetic energy (dropping then climbing then dropping etc.) far more than the more classical styles in which 'trimming' (moving transversely) was emphasized. But even in the modern style, trim is utilized extensively, especially when the surfer is able to get himself in the “pocket” or “barreled”. Climbing and dropping isn't really an option is these situations, all of his propulsion comes from the redirection of the forces of planing.

Which flows make surfboards go

The illustration below is one which  I posted in a prior post,  It seemed to have gotten some traction.

The next illustration, is basically the same, but now I've place a surfer on the plank, and indicated both the force from interaction of the jet and plank, as well as the weight of the surfer/plank. Also, rather than having him move both out of the page and off to the right, here he has oriented his board to move just to the right. (Of course, if the jet doesn't also move of to the right, he'll just move out of the way of the jet.)

In the next illustration, I've removed the drawing of the surfer, but left the force vectors (and flow direction vector), but I've also change the jet shape. Here it's a slit or rectangluar opening, which happens to be the exact length of the projection of the angled plank.

Of course, to keep, or preserve the magnitude and direction of the force I've had to change the nature of the jet, perhaps decreasing its velocity. (Remember that the resultant force on the plank will be proportional to both the flow's speed squared, and the area impacting the plank. see earlier posts.)

Also, it's likely the surfer will have had to readjust his posture or position on the plank to accommodate the new force distribution.

But again, unless the jet slit moves with the plank, the surfer/plank will just slip off the right end.

In the next illustration, I've extended the jet slit in both directions. So now the surfer/plank can continue to move to the right. (The slit can be extended as far as you like.)

In this latest illustration, I've indicate (in dashed circles) two area of interest, the leading edge of the plank, and the trailing edge. The lines emanating from these two zones are meant to be suggestive of the edges of the jet. Their actual shape will depend on both the transverse speed of the plank as well as the speed of the flow (in the jet).

This next illustration, illustrates how they might vary for a given flow -i.e. hold the flow speed constant but change the transverse speed of the plank.

In this last illustration we have effectively two flows operating, one from the jet impacting the bottom of the plank and that from the transverse motion of the plank. It's only the jet flow that makes the “plank go” in this case. (That's not to say the transverse flow won't have consequences.)

A slight beside on design

This next illustration, is an attempt to begin to bring this all back to a what is happening on a wave-face. Perhaps you can visualize it as if the plank is now experiencing a much thicker flow, that is the jet is wider than the plank. But the plank is just on the portion of the flow closest to the viewer. 

The edge of the plank (farthest from the view) is now releasing some of the flow which has impacted with the plank. The hatched area might be the bottom wetted-surface of the plank. (Those lines from the leading edges are in the plane of the jet. They just look like they are coming out of the page because of their curvature.)

At this point its tempting to start removing sections of the plank. But as you do, you might reduce the surface area in play, hence the orientation of the plank (and/or surfer) will have to adjust to maintain the same force. You might also note that the leading edge of the “jet-side” rail offers some interesting design considerations. (See “Rails Plane”) That leading edge and the plane-shape curve will all impact the orientation of the board (assuming that one wishes to maintain a constant force.) The same kinds of considerations are to be made for the trailing 'jet-side' rail.

And even more interesting, the flow up the face increases as you move towards the curl (see “The Decelerating Wave-form”) hence the trail edge or tail of the plank would be experiencing a higher upward flow, which impacts tail design – you can chop more off but still achieve the same force (as the planingforce is proportional to the flow speed squared and area.)

These are not the only considerations that determine rail design or board design, but it's a pretty important start. Perhaps you can begin to see how forward and rear rocker will impact just these simple considerations. Also, this is just for trimming situations.

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There is one more point I'd like to make, and that's regarding the use of the term energy. Energy has magnitude only, whereas force has both magnitude and direction – and force considerations lead to design considerations.

For example, two waves may very well have the same energy, but the forces that can be tapped by the surfer/surfboard in either case will depend on how the wave is shoaling,  which in turn, will determine what the magnitudes and directions of the forces that will be available – and hence design. (See “The Decelerating Wave-form”)

In the end however, you can surf pretty much anything as long as you've got enough planing area ... and the skill to do it.

If you followed the above, especially the case where the plank is moving thru a long thin jet,

it's fun to use the one of the angles as an estimation of the direction of flow under the board.  (In the above I've colored in the water jet so to make the point clearer.)  “Fun”, as in no guarantees, but it offers some insight into the relationships between the the flow up the wave-face and the transverse motion of the plank, and the flow under the board.

The angle (theta) of that forward line in the diagram will be determined by both the flow (speed) of the jet, VF, and the transverse speed at which the plank is moving, VT. In particular, the angle indicated will have the following relationship.

tan( theta) = (VF / VT)

or rearranging,

VF = VT * tan(theta)

The above is pretty crude (for a bunch of reasons!) but its not that bad an estimate.  Basically it implies that the larger the angle theta the larger VF relative to VT, which is what one would expect.

A great video to see this relationship is this Teahupoo video.  (Check out the angle off the wave-side rail once a surfer starts to trim). Then check out some other less extreme surfing videos and look for the angles.

In contrast, the angles in videos or stills of longboards trimming on small waves are often quite small, which suggests that the water moving up the face is much less than the transverse velocity.

Watching how the angle will change in Noseriding videos can also tell you a lot, especially if the fellow is actively walking the board.

The relationship is too crude for accurate measurements of transverse speed or the speed of the flow up the face, but it can tell you a lot about relative nature of both of these speeds and hence the magnitude and a rough sense of the direction of the flow under the board.  (The square root of the sum of the squares of VF and VT will give you a crude estimate of the magnitude. However, the direction of this flow is not relative to the stringer.  You'll have to factor in the orientation of the board.)  This direction is particularly interesting because it provides you with some insight as to how your fins are working -i.e. the flow direction they are experiencing.)

You can take this kind of crude analysis a little futher.  Say the fellow is in trim and either in the barrel or just in front of it. So if you can measure the transverse speed of the curl, it will give you an estimate of the transverse speed of the surfer and from that an estimate of the flow up the face.  (You'll need that angle theta too.)

But as I indicated this is all pretty crude, but it can often provide a sense of how some fin configuration is operating, or even how fast the fellow is traveling.  (Assuming you're also watching posture, position of the board, position of the wave, etc. )

Also, if you're watching video for this kind of thing, check out the white water edge off the rear or trailing edge of the wetted area of the surfboard.  Usually you got a lot of mixing with the 'spray root' (see origin Savistsky diagram) which is just the foam from under the board dropping onto the wave-face and is not obeying the same relationship.  But occasionally it's pretty clear. When it is, notice it's often coming off at a noticiably higher angle –i.e. it's steeper (see The Decelerating Wave-Form.)

Below is a crude illustration of the angles, theta F is the wave-side angle, and theta R is the rear angle. Things will vary, so this is just an illustration of one such situation. The wetted portion of the board is shaded lighter than the wave-face, and I've left out shading that portion of the wave between the two angles.  

Watching this kind of stuff, in particular where that rear angle comes off the board can be pretty revealing. Sometimes the fin configuration is such that it will seemingly determine the rear angle and where that rear angle is formed. 

The Decelerating Wave-Form

A shoaling wave is constantly slowing down.

All shoaling waves decelerate.  This deceleration is often imperceptible to an observer, but it can be quite dramatic - as if the wave seemingly just stopped and "jacked".

The deceleration is the result of a frictional interaction of the water particles currently experiencing the wave action in the very lowest portion of the wave-form with the bottom topography. This slowing down will continue to increase as long as the wave-form continues to move into shallower and shallower water.

Communication between the upper and lower regions of the wave-form is not instantaneous.

The deceleration currently experienced by the lower portions of a shoaling wave is not instantaneously transmitted to the upper regions.  This is why waves break they way they do. The uppermost portions, attempting to continue move forward, slide up and over the lower portions which continue to decelerate.  When the difference in deceleration between the upper and lower portions of the wave-form is sufficiently great - the wave "breaks".

As the wave shoals the height of the wave-form increases.

As a wave starts to shoal, a large portion of the kinetic energy (energy by virtue of relative motion) of the participating water particles is transformed into potential energy (energy by virtue of relative position, here, position in the gravitational field of the Earth) as the upper-most particles continue to slide up and over the lower portions. (Some energy will be lost due to frictional interaction.)  This increase in height results in another acceleration which is of paramount importance to surfers – an accelerating upward flow of water, which on the leading or forward face of the wave-form, manifests itself as a flow up the 'wave-face'.

Drag keeps a surfer connected to the deceleration wave-form.

But if a shoaling  wave-form is constantly slowing down, what exactly keeps surfers from being seemingly launched forward, that is leaving the forward wave-face in the direction in which the wave-form is progressing?

Newton's First Law states,

"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

(If you like you may insert 'constant velocity' for uniform motion. During Newton's time, he and other scientists of his day, saw them as one in the same thing.)  Therefore, if the surfer is to remain connected to a decelerating wave-face, there must be some force or set of forces that similarly slow down the surfer, or similarly decelerate him, at least in the direction in which the wave-form is moving.

There are a number of forces that can be at play here, but the dominant force that keeps a surfer on the wave-face is drag. In particular, the drag which is generated from the interaction of the surfboards wetted-surface (which  might include fins, etc.) and the flow of water past that surface.

Some of the other forces might include wind-resistance (another source of drag), or the surface tension, or that from material interaction (surfboard surface and water in this case). But by far, the largest contributor is the drag generated by the wetted-surface and the flow of the water up the wave-face.

The curl region is decelerating faster than the shoulder region.

The 'curl' (the region where the wave appears to be breaking or where breaking appears to be imminent) is an important region to surfers. Curiously, this region however, relative to the unbroken portions of the wave, is decelerating faster. That is, the 'shoulder' region, that part of the wave-form which has yet to break, is actually moving faster than the curl.  The transition between the two regions generally appears quite smooth and continuous. at least for most of the breaks that surfers frequent. So smooth, as to be almost imperceptible in terms of the difference in deceleration as you move from shoulder to curl.

The flow up the wave-face is greater in the curl region.

And in a manner similar to that described above, the degree of upward acceleration of the wave-form is different for these different regions too. Slowest for the shoulder regions, becoming increasingly more rapid as you move towards the curl.

So surfers have to contend with at least two kinds of acceleration; a deceleration which is greatest in the curl region, and an upward acceleration which is also greatest in the curl region. Both of these accelerations becoming progressively lesser magnitude as you move out onto the shoulder.

As mentioned above, the dominant forces that keeps a surfer on the wave-face is drag, and that drag is generated by the interaction of the surfboards wetted-surfaces with the flow of water up the wave-face. So the acceleration of the flow up the wave-face is used in part as a way for the surfer to stay connected to the wave-form - allowing him to decelerate in kind as the wave continues to shoal.